相关论文: The SYZ conjecture for singular moduli spaces of s…

The aim of this work is to give a description of the locally trivial monodromy group of irreducible symplectic varieties arising from moduli spaces of semistable sheaves on Abelian surfaces with non-primitive Mukai vector. The outcome is…

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from…

Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the Shafarevich conjecture for irreducible symplectic varieties of fixed deformation class. We also observe that the second…

We show that the moduli spaces of sheaves on a projective K3 surface are irreducible symplectic varieties, and that the same holds for the fibers of the Albanese map of moduli spaces of sheaves on an Abelian surface.

In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…

The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non--generic polarization, with respect…

Moduli spaces of stably irreducible sheaves on Kodaira surfaces belong to the short list of examples of smooth and compact holomorphic symplectic manifolds, and it is not yet known how they fit into the classification of holomorphic…

We investigate the moduli spaces of one- and two-dimensional sheaves on projective K3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability. We can exclude the…

Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the finiteness of twists of irreducible symplectic varieties via a fixed finite field extension of characteristic $0$. The main…

We study symplectic varieties defined over fields of positive characteristics, especially the supersingular ones, generalizing the theory of supersingular K3 surfaces. In this work, we are mainly interested in the following two types of…

We show that there is a good notion of irreducible sympelectic varieties of $\mathrm{K3}^{[n]}$-type over an arbitrary field of characteristic zero or $p > n + 1$. Then we construct mixed characteristic moduli spaces for these varieties.…

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces…

In this paper, we show the moduli spaces of stable sheaves on K3 surfaces are irreducible symplectic manifolds, if the associated Mukai vectors are primitive. More precisely, we show that they are related to the Hilbert scheme of points. We…

We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky's theory of hyperholomorphic sheaves and a study of the cohomology…

This paper deals with symplectic varieties which do not have symplectic resolutions. Some moduli spaces of semi-stable torsion-free sheaves on a K3 surface, and symplectic V-manifolds are such varieties. We shall prove local Torelli theorem…

Symplectic involutions of a K3 surface are those involutions which leave the holomorphic 2-form invariant. We show, as predicted by Bloch's conjecture, that they act trivially on the CH_0 group of the K3 surface. This was recently proved by…

In this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If $S$ is a K3, $v=2w$ is a Mukai vector on $S$, where $w$ is primitive and $w^{2}=2$, and $H$ is a $v-$generic polarization on $S$, then the moduli…

In this paper we study monodromy operators on moduli spaces $M_v(S,H)$ of sheaves on K3 surfaces with non-primitive Mukai vectors $v$. If we write $v=mw$, with $m>1$ and $w$ primitive, then our main result is that the inclusion $M_w(S,H)\to…

We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…